Optical substrate with modulated structure

ABSTRACT

There is provided an optical substrate. The optical substrate includes at least one surface. The at least one surface includes at least one optical structure having a shape and dimensions, wherein the shape and dimensions of each optical structure represents in part a modulation of a corresponding idealized structure. The shape and dimensions of each of the at least one optical structure are determined in part by at least one randomly generated component of modulation wherein the modulation of each of the at least one optical structure is limited by a neighboring optical structure comprised by the surface.

BACKGROUND OF THE INVENTION

The invention relates to an optical substrate with modulated structureson its surface. The optical substrate can be a light modulatingsubstrate of a flat panel display backlight, such as a liquid crystaldisplay (LCD) backlight.

A backlight illuminates a liquid crystal based display panel to providea uniformly intense light distribution over the entire plane of the LCDdisplay panel. A backlight system typically incorporates a light pipe tocouple light energy from a light source to the LCD panel. An array ofdiffusing elements can be disposed along one surface of the light pipeto scatter incident light rays toward an output plane. The output planecouples the light rays into and through the LCD panel. The backlight canuse a light modulating optical substrate with prismatic or texturedstructures to direct light along a viewing axis, usually normal to thedisplay and to spread illumination over a viewer space. The backlightcan use a plurality of optical substrates, stacked and arranged so thatthe prismatic or textured surfaces are perpendicular to one another andare sandwiched between optical modifying films known as diffusers. Thebrightness enhancement optical substrate and diffuser film combinationsenhance the brightness of the light viewed by a user and reduce thedisplay power required to produce a target illumination level.

It may be advantageous to modulate the structural order of an opticalsubstrate to hide manufacturing defects and to decrease optical couplinginterference such as Moiré interference. For example, copending patentapplication Ser. No. 10/248,099, filed Dec. 18, 2002 disclosesmodulating a prism structure of an optical substrate from a nominallinear path in a lateral direction (direction perpendicular to theheight) by applying a nonrandom, random (or pseudo random) amplitude andperiod texture. The disclosure of application Ser. No. 10/248,099 isincorporated herein by reference in its entirety. Application Ser. No.10/248,099 discloses a method which reduces interference Moiré effects.However, for a given nominal texture pitch, a peak to valley depth ofthe structures which have been modulated is approximately 100% greaterthan for the un-modulated structure of the same pitch. The greater peakto valley depth for the modulated structures may require a greateroverall device thickness to preserve mechanical integrity. The nominaltexture pitch is the center to center distance between adjacentstructures, such as prisms, on the substrate, the peak to valley depthis the difference between peak and valley.

There is a need for an optical structure on light managed substrate withreduced interference and with preserved mechanical integrity.

SUMMARY OF THE INVENTION

According to one embodiment of the invention there is provided anoptical substrate. The optical substrate comprises at least one surface,said at least one surface comprising at least one optical structurehaving a shape and dimensions, wherein the shape and dimensions of eachoptical structure represents in part a modulation of a correspondingidealized structure, and wherein said shape and dimensions of each ofsaid at least one optical structure is determined in part by at leastone randomly generated component of modulation wherein the modulation ofeach of said at least one optical structure is limited by a neighboringoptical structure comprised by the surface.

According to one aspect of this embodiment, the at least one opticalstructure represents an idealized prismatic structure following asurface path modulated by a mathematical function (1)y _(i) =A _(i) sin{φλ−Φ_(i) }+S _(i)  (1)defined relative to a segment C of a coordinate system, wherein i is aninteger indicative of the i^(th) surface path, y_(i) is an instantaneousdisplacement of the path relative to C on the i^(th) path, A_(i) is anamplitude scaling factor of the i^(th) path relative to C, S_(i) is ashift in a starting position of y_(i), φ is a number between zero and 2πinclusive, λ is a wavelength which is a real number, Φ_(i) is a phasecomponent for the i^(th) path, whereinΦ_(i)=Φ_(i−1) +Q _(i) Δ+R _(i)δ  (2)where Q_(i) is randomly or pseudo randomly chosen number having a valueof 1 or −1 and R_(i) is a continuous random variable between −1 and 1,each defined for the i^(th) path, where Δ and δ are real numbers thatdefine a magnitude of a phase stepping component and a magnitude of aphase dither component, respectively.

According to another aspect of this embodiment, the at least one opticalstructure represents an idealized prismatic structure following asurface path modulated by a mathematical function (3a)

$\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}\sin\left\{ {{\phi\;\lambda_{k}} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {3a} \right)\end{matrix}$defined relative to a segment C of a coordinate system, wherein i is aninteger indicative of the i^(th) surface path, y_(i) is an instantaneousdisplacement of the path relative to C on the i^(th) path, A_(i,k) isthe k^(th) amplitude scaling factor of the i^(th) path relative to C,and S_(i) is a shift in a starting position of y_(i), φ is a numberbetween zero and 2π inclusive, where n is an integer greater than 1,each wavelength λ_(k) is a real number, Φ_(i,k) is the k^(th) phasecomponent of the i^(th) path, whereinΦ_(i,k)=Φ_(i−1,k) +Q _(i,k) Δ+R _(i,k)δ  (3b)Q_(i,k) is the k^(th) randomly or pseudo randomly chosen number having avalue of 1 or −1 for the i^(th) path, R_(i,k) is the k^(th) continuousrandom variable having a value between −1 and 1 for the i^(th) path, andΔ and δ are real numbers that define a magnitude of a phase steppingcomponent and a magnitude of a phase dither component, respectively.

According to another aspect of this embodiment, the at least one opticalstructure represents an idealized prismatic structure following asurface path modulated by a mathematical function (4a)

$\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}\sin\left\{ {{\phi\lambda}_{k} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {4a} \right)\end{matrix}$wherein ƒ is a periodic function defined relative to a segment C of acoordinate system, wherein i is an integer indicative of the i^(th)surface path, y_(i) is an instantaneous displacement of the pathrelative to C on the i^(th) path, A_(i,k) is the k^(th) amplitudescaling factor of the i^(th) path relative to C, and S_(i) is a shift ina starting position of y_(i), φ is a number between zero and 2πinclusive, where n is an integer greater than 1, each wavelength λ_(k)is a real number, Φ_(i,k) is the k^(th) phase component of the i^(th)path, whereinΦ_(i,k)=Φ_(i−1,k) +Q _(i,k) Δ+R _(i,k)δ  (4b)Q_(i,k) is the k^(th) randomly or pseudo randomly chosen number having avalue of 1 or −1 for the i^(th) path, R_(i,k) is the k^(th) continuousrandom variable having a value between −1 and 1 for the i^(th) path, andΔ and δ are real numbers that define a magnitude of a phase steppingcomponent and a magnitude of a phase dither component, respectively.

According to another aspect of this embodiment, the at least one opticalstructure represents an idealized prismatic structure following asurface path modulated by a mathematical functiony _(i) =A _(i)[(1−m)r _(i)(φ)+m r _(i−1)(φ)]+S _(i)wherein i and i−1 are indicative of an i^(th) and a (i−1)^(th) path,respectively, the i^(th) and the (i−1)^(th) paths being adjacent paths,the i^(th) and the (i−1)^(th) path amplitudes being mixed, wherein partof a random vector for y_(i−1) is added to y_(i) for the i^(th) path,wherein r_(i)(φ) is a band-limited random or pseudo random function of φfor each i^(th) path, r_(i)(φ) having a continuously varying valuebetween −1 and 1; φ is φ to 2π inclusive; m is a scalar mixing parameterwith a value between 0 and 1; A_(i) is an amplitude scaling parameter;and S_(i) is a shift in a starting position of y_(i).

According to another embodiment of the invention there is provided abacklight display device. The backlight display device comprises: alight source for generating light; a light guide for guiding the lighttherealong including a reflective surface for reflecting the light outof the light guide; and an optical film. The optical film comprises: atleast one surface, the at least one surface comprising at least oneoptical structure having a shape and dimensions, wherein the shape anddimensions of each optical structure represents in part a modulation ofa corresponding idealized structure, and wherein said shape anddimensions of each of said at least one optical structure is determinedin part by at least one randomly generated component of modulationwherein the modulation of each of said at least one optical structure islimited by a neighboring optical structure comprised by the surface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a three dimensional view of a backlight display device;

FIG. 2 is a flow chart showing a method of machining a surface of aworkpiece wherein the workpiece is a master drum;

FIG. 3 is a flow chart showing a method of machining a surface of aworkpiece wherein the workpiece is on a master plate;

FIG. 4 is a diagram of a master drum having a random or pseudo randompattern therein following a generally spiral-like or threaded path;

FIG. 5 is a diagram of a master drum having a random or pseudo randompattern therein over generally concentric paths;

FIG. 6 is a diagram of a master plate having a random or pseudo randompattern therein following a generally sawtooth or triangular path;

FIG. 7 is a diagram of a master plate having a random or pseudo randompattern therein along a series of paths;

FIG. 8 is a diagram of a cross section of a cutting tool in the natureof a prismatic structure;

FIG. 9 is a diagram of the prismatic cutting tool of FIG. 8 havingcompound angled facets;

FIG. 10 is a graphical representation of the magnitude of the powerspectral density of the randomized surface of the workpiece as afunction of spatial frequency;

FIG. 11 is a top view of a randomized surface of a workpiece accordingto an embodiment of the invention;

FIG. 12 is a graphical representation of a plurality of paths due to aplurality of cutting passes over the surface of the workpiece;

FIG. 13 is a schematic representation of a system and apparatus formachining the surface of a work piece in communication over acommunications or data network with remote locations;

FIG. 14 is a graphical representation of mathematical functions;

FIG. 15 is a schematic diagram of a master machining system with a fasttool servo for cutting grooves having lateral variations in the surfaceof a workpiece;

FIG. 16 is a depiction of a cutting gradient introduced into the surfaceof the machined surface of the workpiece

FIG. 17 and FIG. 18 are graphs of slide feed distance to circumferencedistance;

FIG. 19 is a surface height map;

FIG. 20 is an autocorrelation of the FIG. 19 surface; and

FIG. 21 is a surface height (depth) histogram.

DETAILED DESCRIPTION OF THE INVENTION

According to one aspect of the invention, a phase step limitedmodulation algorithm may be applied to modulate a regular function ofthe structure of an optical structure so as to provide an opticalstructure with a modulated structure. The resulting optical structurecan comprise a randomly modulated optical structure defined by amodulation algorithm that modulates a parameter of the regular function,such as the phase, although the invention is not limited to modulatingthe phase. Preferably the modulation values are quantized and limitedwithin intervals of adjacent paths of the optical structures.

Features of the invention will become apparent from the drawings andfollowing detailed discussion, which by way of example withoutlimitation describe preferred embodiments of the invention.

FIG. 1 is a perspective view of a backlight display device 10. Thebacklight display device 10 comprises an optical source 12 forgenerating light 16. A light guide 14 guides light 16 along its bodyfrom the optical source 12. The light guide 14 contains disruptivefeatures that permit the light 16 to escape the light guide 14. Suchdisruptive features may include a surface manufactured from a masterhaving a machined cutting gradient. A reflective substrate 18 positionedalong the lower surface of the light guide 24 reflects light 16 escapingfrom a lower surface of the light guide 14 back through the light guide16 and toward an optical substrate 24. The optical substrate 24 may befabricated from a positive or negative master having a nonrandomized,randomized or pseudo randomized surface 22 prepared according to theinvention.

At least one optical substrate 24 is receptive of the light 16 from thelight guide 14. The optical substrate 24 comprises a planar surface 20on one side and the randomized three dimensional surface 22 on thesecond opposing side. Optical substrate 24 receives light 16 and turnsand diffuses the light 16 in a direction that is substantially normal tothe optical substrate 24 as shown. A diffuser 28 is located above theoptical substrate 24 to provide diffusion of the light 16. For example,the diffuser 28 can be a retarder film that rotates the plane ofpolarization of light exiting the optical substrate 24 to match thelight to the input polarization axis of the LCD. The retarder film maybe formed by stretching a textured or untextured polymer substrate alongan axis in the plane of the substrate 24.

FIG. 1 shows a single substrate 24. However, a backlight display devicemay comprise a plurality of substrates 24 positioned, one above theother, in a crossed configuration with respective prismatic structures26 positioned at angles to one another. Yet further, one or both sidesof the substrates 24 may comprise prismatic structures 26. The opticalsubstrate 24 may be formed by a process of electroforming from a workpiece master that is fabricated as herein described below. The opticalsubstrate 24, however, is not limited to any particular fabricationprocess.

FIG. 2 illustrates a method of machining a surface of a work piece suchas a master shown generally at 100. The work piece can be a master tomodel an optical substrate 24 having a nonrandomized, randomized orpseudo randomized surface 22 according to the invention. In FIG. 2, anoise signal 102 is band pass filtered 104 and provided as input to afunction generator 106. A modulating mathematical function, such as asinusoidal wave form is provided by the function generator 106 as inputto a servo mechanism 108. The noise signal 102, the bandpass filter 104and the function generator 106 can be replaced by a computer systemequipped with the appropriate signal processing software anddigital-to-analog conversion board so as to generate the input signal tothe servo mechanism 108.

The servo mechanism 108 directs relative movement between the cuttingtool 110 and the surface of a drum 112 rotating at an angular velocityof ω in a cylindrical coordinate system (r,θ,z). As the drum 112 rotatesat angular velocity ω the cutting tool 110 moves relative to the drum112 along the drum axis, z, and may be driven back and forth with afrequency of up to about 10,000 Hz parallel to the z-axis of drum 112(along the y-axis of the tool). The tool 110 may be driven back andforth parallel to the axis of the drum in a random or pseudo randomnature in an embodiment of the invention. Cutting tool 110 is incontinuous contact with the surface of rotating drum 110 to cut ormachine a randomized spiral-like or threaded pattern 116 (FIG. 4) ofnominal pitch, P. A two axis cutting tool 110 moves back and forthparallel to the drum axis 112 and also perpendicular to the drumsurface.

Alternatively, the cutting tool 110 may be in contact with the surfaceof a flat plate 114 as seen in FIG. 6, moving at a velocity of ν in arectilinear coordinate system (x,y,z). As plate 114 moves at velocity θ,the cutting tool 110 is driven back and forth across the plate in arandom or pseudo random nature to cut or machine a randomized triangularpattern 122 (FIG. 6), for example, into the surface of the plate 114.

In an alternative embodiment of the invention, as seen in FIG. 5, thedrum 112 need not move along the z axis as the drum 112 rotates. Assuch, the cutting tool machines a randomized or pseudo randomizedpattern along a series of concentric rings 118 in the surface of thedrum 112 whereby the cutting tool returns to a starting point 122 foreach cutting pass. To achieve good cutting quality, a control system canallow the cutting tool 110 to repeat the pattern of any i^(th) cuttingpass for the number of revolutions depending upon the desired final cutdepth and in-feed rate. When the cutting tool 110 finishes the number ofrevolutions and returns to the starting point 122 of the (i−1)^(th)cutting pass, the cutting tool 110 is shifted or stepped a distanceS_(i), to be positioned at position S_(i) for the next, or i^(th),cutting pass.

The cutting tool 110 may have more than one axis of travel. For exampleit can have three axes of travel r, θ, z in cylindrical coordinates andx, y, z in rectilinear coordinates. Such additional axes allow for thecutting of toroidal lens type structures when using a radiused cuttingtool 110 or allow for a gradient in the cut along the cut length, forexample. Translational axes r, θ, z and x, y, z will also allow forintroducing a cutting gradient into the pattern machined into thesurface of the workpiece 112, 114 for subsequent cutting passes. Such acutting gradient is best seen with reference to FIG. 16. In FIG. 16, thei^(th) cutting pass has a thickness or width of w_(i) and the (i+1)^(th)cutting pass has a thickness of w_(i+1) where w_(i) is greater or lessthan w_(i+1). In general, the n^(th) cutting pass has a width of w_(n)where w_(n) is greater or less than w_(i), whre i≠n. It will beunderstood that the change in the thickness in the cutting pattern insubsequent cutting passes may be nonrandom, random or pseudo random.Additional rotational degrees of freedom (e.g., pitch 152, yaw 150 androll 154, FIGS. 2–7) may be used to change the angular orientation ofthe cutting tool 110 with respect to the surface of the workpiece 112,114, thus changing the geometry of the facets machined into the mastersurface.

The randomized or pseudo randomized pattern machined into the surface ofthe work piece 112, 114 is in the nature of a number of paths ofidealized structure, the idealized structure, hourly paths defined bymathematical function defined over a segment, C, of a coordinate systemand characterized by a set of random or pseudorandom phase or otherparameters. For a rotating drum 112, the segment, C, over which themathematical function is defined is the circumference of the drum 112.For a moving plate 114, the segment, C, over which the mathematicalfunction is defined is a width or length of the plate 114. An exemplarymathematical function is a function that is periodic over the segment C,such as that of the sine wave of Equation 1:y _(i) =A _(i) sin{φλ−Φ_(i) }+S _(i)  (1)defined relative to the segment C, i is an integer indicative of thei^(th) surface path, y_(i) is an instantaneous displacement of the pathrelative to C on the i^(th) path, A_(i) is an amplitude scaling factorof the i^(th) path relative to C, and S_(i) is a shift in a startingposition of y_(i). φ is a number between zero and 2π inclusive, and λ isa wavelength which is a real number. Φ_(i) is a phase component for thei^(th) path, whereinΦ_(i=Φ) _(i−1) +Q _(i) Δ+R _(i)δ  (2)where Q_(i) is randomly or pseudo randomly chosen number having a valueof 1 or −1 and R_(i) is a continuous random variable between −1 and 1,each defined for the i^(th) path. Δ and δ are real numbers that define amagnitude of a phase stepping component and a magnitude of a phasedither component, respectively. The nominal y position S_(i) is the yposition without any modulation of the path.

By limiting the absolute value of Q_(i)Δ+R_(i)δ to less than π radiansthe depth of the patterned surface is reduced since adjacent tool pathsare not permitted to be π radians out of phase.

In the more general case where multiple wavelengths are usedsimultaneously at each path, the idealized prismatic structure followinga surface path is modulated by a mathematical function (3a)

$\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}\sin\left\{ {{\phi\;\lambda_{k}} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {3a} \right)\end{matrix}$defined relative to the segment C, wherein i is an integer indicative ofthe i^(th) surface path, y_(i) is an instantaneous displacement of thepath relative to C on the i^(th) path. A_(i,k) is the k^(th) amplitudescaling factor of the i^(th) path relative to C, and S_(i) is a shift ina starting position of y_(i), φ is a number between zero and 2πinclusive, n is an integer greater than 1, and wavelength λ_(k) is areal number. Φ_(i,k) is the k^(th) phase component of the i^(th) path,whereinΦ_(i,k)=Φ_(i−1,k) +Q _(i,k) Δ+R _(i,k)δ  (3b)Q_(i,k) is the k^(th) randomly or pseudo randomly chosen number having avalue of 1 or −1 for the i^(th) path, R_(i,k) is the k^(th) continuousrandom variable having a value between −1 and 1 for the i^(th) path, andΔ and δ are real numbers that define a magnitude of a phase steppingcomponent and a magnitude of a phase dither component, respectively. Thenominal y position S_(i) is the y position without any modulation of thepath.

An even more general case for the function y_(i) is provided by:

$\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}f\mspace{14mu}\left\{ {{\phi\lambda}_{k} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {4a} \right) \\{\Phi_{i,k} = {\Phi_{{i - 1},k} + {Q_{i,k}\Delta} + {R_{i,k}\delta}}} & \left( {4b} \right)\end{matrix}$where periodic function ƒ has been substituted for the sine function ofequation (3a) in equation (4a). Such periodic functions include forexample the well known triangular function, sawtooth function and squarewave function.

It will be understood that the mathematical function ƒ referred to abovemay be any mathematical function ƒ that can be programmed into acomputer numerically controlled (CNC) machine. Such functions includefor example the well known triangular function, sawtooth function andsquare wave function (FIG. 14) each of which may be randomly modulatedin phase.

In another embodiment the paths of the idealized structure can belimited by allowing mixing of the amplitude adjacent tool paths. Supposethat y_(i) is given byy _(i) =Ar _(i)(φ)+S _(i)  (5)where r_(i)(φ) is a band limited random or pseudo random function of φfor each ith path with a continuously varying value between −1 and 1, Aiis an amplitude constant, Si is the shift in starting position and thenominal y position for the ith path, and φ is in the range of 0 to 2π.The mixing may be introduced by use of a mixing parameter, m, such thatpart of the random vector for the (i−1)th random function is added to yifor the ith path as given in equation 6.y _(i) =A[(1−m)r _(i)(φ)+m r _(i−1)(φ)]+S _(i)  (6)where m is a scalar mixing parameter with a value between 0 and 1.

Referring to FIGS. 8 and 9, the cutting tool 110 may comprise aprismatic structure having a cross section which may include straightfacets 130, 132 intersecting at a tip 134 at a peak angle of 2θ. Theprismatic shaped cutting tool 110 may also comprise linear segments 130,132 of the facets 132, 134 resulting in a compound angled prism. Thecompound angle prism has a first facet 138 at an angle of (α and asecond facet 140 at an angle of β with respect to a base 142 of theprism 110. As best understood from FIGS. 8 and 9, the cutting tool 110may have a cross section with a rounded peak 134 or radius “r.” Ingeneral the cutting tool can have a cross section of any manufacturableshape.

An example of the equipment used to machine the surface of the workpiece112, 114 in the invention is shown in FIG. 13. Machining the surface ofthe workpiece 112, 114 can be accomplished by computer numericallycontrolled (CNC) milling or cutting machine 202. The machine 202includes cutting tool 110, which is controlled by a software program 208installed in a computer 204. The software program 208 controls themovement of the cutting tool 110. The computer 204 is interconnected tothe CNC milling machine 202 by an appropriate cabling system 206. Thecomputer 204 includes storage medium 212 for storing software program208, a processor for executing the program 208, keyboard 210 forproviding manual input to the processor, a display 218 and a modem ornetwork card for communicating with a remote computer 216 via theInternet 214 or a local network.

FIG. 15 illustrates a master machining system 400 with a fast tool servofor cutting workpiece grooves with lateral variations. An input/outputdata processor 402 provides cutting commands to a digital signalprocessing (DSP) unit 404 that supplies a signal to a digital-to-analog(DA) conversion device 406. Voltage amplifier 408 receives a signal fromthe DA converter 406 and drives fast tool servo mechanism 410 to directthe motion of cutting tool 110. Cutting tool position probe 412 senses aposition of the cutting tool 110 and provides a signal indicative of theposition to a sensor amplifier 418. Amplifier 418 amplifies the signal.The amplified signal is directed to analog-to-digital (A/D) converter420. Lathe encoder 414 determines the position of the workpiece (e.g.,drum 112) and provides a feedback signal to the A/D converter 420. TheA/D converter thus provides a feedback signal indicative of the positionof the cutting tool 110 and the position of the workpiece 112, 114 asoutput to the digital signal processing unit 404. The DSP unit 404provides a processed signal to the input/output processor 402.

The system 400 can provide a randomly or pseudo randomly machinedworkpiece surface. In operation, computer 204 with installed softwareprogram 208 is in communication with the CNC milling machine 202. Anoperator may provide input value A_(i) to personal computer 204. Theoperator input can be provided manually by typing the A_(i) value usingkeyboard 210. Controlling mathematical function or functions may bestored within the computer's memory or may be stored on a remotecomputer 216 and accessed via the Internet 214 or via a local network.

In operation, the A_(i) value is provided to the CNC machine 202. Thencutting element 110 of the CNC machine 202 begins to mill the workpiece112, 114 according to commands provided by the software program 208 thatprovides coordinates to direct movement of the cutting tool 110.Additionally, the program 208 controls depth of the milling process. Theprocess provides a nonrandomized, randomized or pseudo randomizedworkpiece that can be used as a “positive” or a “negative” master toproduce an optical substrate. For example, the optical substrate 24 ofFIG. 1 can be generated by forming a negative or positive electroformover the surface of the workpiece 112, 114. Alternatively, a moldingmaterial can be used to form a replica of an original positive ornegative master—for example, an ultraviolet (UV) or thermal curing epoxymaterial or silicon material. Any of these replicas may be used as amold for a plastic part. Embossing, injection molding, or other methodsmay be used to form the parts.

Autocorrelation function, R(x,y), is a measure of the randomness of asurface in electro metrology. Over a certain correlation length, l_(c),however, the value of an autocorrelation function, R(x,y), drops to afraction of its initial value. An autocorrelation value of 1.0, forinstance, would be considered a highly or perfectly correlated surface.The correlation length, l_(c), is the length at which the value of theautocorrelation function is a certain fraction of its initial value.Typically, the correlation length is based upon a value of 1/e, or about37 percent of the initial value of the autocorrelation function. Alarger correlation length means that the surface is less random than asurface with a smaller correlation length.

In some embodiments of the invention, the autocorrelation function valuefor the three-dimensional surface of the optical substrate 24 drops toless than or equal to 1/e of its initial value in a correlation lengthof about 1 cm or less. In still other embodiments, the value of theautocorrelation function drops to 1/e of its initial value in about 0.5cm or less. For other embodiments of the substrate the value of theautocorrelation function along length l drops to less than or equal to1/e of its initial value in about 200 microns or less. For still otherembodiments, the value of the autocorrelation function along width wdrops to less than or equal to 1/e of its initial value in about 11microns or less.

According to an embodiment of this invention, randomization ofstructures is accomplished with phase modulation only. For example,using randomization of the phase of a sine wave, or other periodicfunction, a modulated path can be achieved by applying a randomizationalgorithm to succeeding adjacent paths of the structures. A randomnumber, such as a binary random number having only two possible values,is computer generated between each path. The number is then compared toa threshold. If the number is greater that the threshold then the phaseof the next path is advanced by a constant, if the number is less thanor equal to the constant, then the phase of the next path is delayed bya constant. As an example, the threshold could be 0.5 and the randomnumber could be a binary number with possible values +1 and −1. Thenumber of times that phase is changed by the randomization algorithm isat least once, and may be more than once. The present invention is notlimited to a particulare selected constant for changing the phase. Theselected constant may be 120° or 90°, for example. With each next pass,the next phase is advanced or delayed by 120° (or 90°) according towhether the random number exceeds or is less than the constant. Ofcourse different constants may be used, or a range of values withincertain intervals, either symmetrical or unsymmetrical, can be used asthreshold values. As an example of assymetrical constants, the constantmay be +120° and −90°, for example.

The phase only limited modulation approach creates a highly randomizedsurface that has less overhead in depth.

FIG. 17 is an illustration of an embodiment according to equation 5.Here “slide feed distance” is S_(i)−S_(i−1) and “Random signal interval”is the amplitude of A_(i) r_(i)(φ). In this embodiment, y_(i) may be adigital signal that is sampled along the drum circumference.

FIG. 18 is an illustration of the embodiment according to equations 1 to3 but illustrated with a sawtooth wave for simplicity instead of a sine.

FIG. 19 is a replicate surface height map of a two wavelength phaseshifting design occurring according to equation 4a to 4c. The surfaceshown is a negative copy of the drum surface. Here S_(i)−S_(i−1)=45 um,n=2, A₁+A₂=22.5 um, λ₁=170 um, λ₂=20 mm, δ₁=0, Δ₁=π/3 radians, δ₂=0,Δ₂=π/3 radians and the prism peak angle is 90 degrees.

FIG. 20 is an autocorrelation of the surface in FIG. 19 for a profile ofthe surface in a direction perpendicular to the circumferentialdirection. Note the autocorrelation length is less than 200 um.

FIG. 21 is the surface height (depth) histogram for the surface shown isFIG. 19. Note that total depth of the surface is 33 um. Here, usingprevious randomization algorithms would result in a peak to valleyheight of 45 um. If for example the desired peak to valley modulation is45 um (in plane) then the modulation approach can be decomposed to afirst component that is phase limited and a second component that isnot. The height to pitch advantage of the invention will be partiallyreduced depending on the ratio of the two components and the phaselimiting parameter(s).

The height to pitch ratio will depend on the range of the phase stepsallowed. A small phase step (5 degrees) will provide less randomizationand a large phase step (170 degrees) will provide a deeper structure.+/−50–140 degrees is the preferred range.

While preferred embodiments of the invention have been described, thepresent invention is capable of variation and modification and thereforeshould not be limited to the precise details of the Examples. Theinvention includes changes and alterations that fall within the purviewof the following claims.

1. An optical substrate comprising: at least one surface, said at leastone surface comprising at least one optical structure having a shape anddimensions, wherein the shape and dimensions of each optical structurerepresents in part a modulation of a corresponding idealized structure,and wherein said shape and dimensions of each of said at least oneoptical structure is determined in part by at least one randomlygenerated component of modulation wherein the modulation of each of saidat least one optical structure is limited by a neighboring opticalstructure comprised by the surface.
 2. An optical substrate according toclaim 1 wherein said at least one optical structure represents anidealized prismatic structure following a surface path modulated by amathematical function (1)y _(i) =A _(i)sin{φλ−Φ_(i) }+S _(i)  (1) defined relative to a segment Cof a coordinate system, wherein i is an integer indicative of the i^(th)surface path, y_(i) is an instantaneous displacement of the pathrelative to C on the i^(th) path, A_(i) is an amplitude scaling factorof the i^(th) path relative to C, S_(i) is a shift in a startingposition of y_(i), φ is a number between zero and 2π inclusive, λ is awavelength which is a real number, Φ_(i) is a phase component for thei^(th) path, whereinΦ_(i)=Φ_(i−1) +Q _(i) Δ+R _(i)δ  (2) where Q_(i) is a randomly or pseudorandomly chosen number having a value of 1 or −1, R_(i) is a continuousrandom variable between −1 and 1, each defined for the i^(th) path, andΔ and δ are real numbers that define a magnitude of a phase steppingcomponent and a magnitude of a phase dither component, respectively. 3.An optical substrate according to claim 1 wherein said at least oneoptical structure represents an idealized prismatic structure followinga surface path modulated by a mathematical function (3a) $\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}\sin\left\{ {{\phi\;\lambda_{k}} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {3a} \right)\end{matrix}$ defined relative to a segment C of a coordinate system,wherein i is an integer indicative of the i^(th) surface path, y_(i) isan instantaneous displacement of the path relative to C on the i^(th)path, A_(i,k) is the k^(th) amplitude scaling factor of the i^(th) pathrelative to C, S_(i) is a shift in a starting position of y_(i), φ is anumber between zero and 2π inclusive, n is an integer greater than 1,each wavelength γ_(k) is a real number, Φ_(i,k) is the k^(th) phasecomponent of the i^(th) path, whereinΦ_(i,k)=Φ_(i−1,k) +Q _(i,k) Δ+R _(i,k)δ  (3b) Q_(i,k) is the k^(th)randomly or pseudo randomly chosen number having a value of 1 or −1 forthe i^(th) path, R_(i,k) is the k^(th) continuous random variable havinga value between −1 and 1 for the i^(th) path, and Δ and δ are realnumbers that define a magnitude of a phase stepping component and amagnitude of a phase dither component, respectively.
 4. An opticalsubstrate according to claim 1 wherein said at least one opticalstructure represents an idealized prismatic structure following asurface path modulated by a mathematical function (4a) $\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}f\mspace{14mu}\left\{ {{\phi\lambda}_{k} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {4a} \right)\end{matrix}$ wherein ƒ is a periodic function defined relative to asegment C of a coordinate system, wherein i is an integer indicative ofthe i^(th) surface path, y_(i) is an instantaneous displacement of thepath relative to C on the i^(th) path, A_(i,k) is the k^(th) amplitudescaling factor of the i^(th) path relative to C, S_(i) is a shift in astarting position of y_(i), φ is a number between zero and 2π inclusive,n is an integer greater than 1, each wavelength λ_(k) is a real number,Φ_(i,k) is the k^(th) phase component of the i^(th) path, whereinΦ_(i,k)=Φ_(i−1,k) +Q _(i,k) Δ+R _(i,k)δ  (4b) Q_(i,k) is the k^(th)randomly or pseudo randomly chosen number having a value of 1 or −1 forthe i^(th) path R_(i,k) is the k^(th) continuous random variable havinga value between −1 and 1 for the i^(th) path, and Δ and δ are realnumbers that define a magnitude of a phase stepping component and amagnitude of a phase dither component, respectively.
 5. The substrate ofclaim 3 where 0≦Δ<(0.95π) radians.
 6. The substrate of claim 3 where0≦δ<(0.5π) radians.
 7. The substrate of claim 3 where 0≦Δ<(0.95π)radians and 0≦δ<(0.5π) radians.
 8. An optical substrate according toclaim 1 wherein said at least one optical structure represents anidealized prismatic structure following a surface path modulated by amathematical functiony _(i) =A _(i)[(1−m)r _(i)(φ)+m r _(i−1)(φ)]+S _(i) wherein i and i−1are indicative of an i^(th) and a (i−1)^(th) path, respectively, thei^(th) and the (i−1)^(th) paths being adjacent paths, the i^(th) and the(i−1)^(th) path amplitudes being mixed, wherein part of a random vectorfor y_(i−1) is added to y_(i) for the i^(th) path, wherein r_(i)(φ) is aband-limited random or pseudo random function of φ for each i^(th) path,r_(i)(φ) has a continuously varying value between −1 and 1; φ is 0 to 2πinclusive; m is a scalar mixing parameter with a value between 0 and 1;A_(i) is an amplitude scaling parameter; and S_(i) is a shift in astarting position of y_(i).
 9. The optical substrate of claim 1, whereinthe optical substrate comprises an optically transparent film having asecond surface opposite to the first surface, the second surface beingsmooth.
 10. The optical substrate of claim 2, wherein the opticalsubstrate comprises an optically transparent film having a secondsurface opposite to the first surface, the second surface being smooth.11. The optical substrate of claim 3, wherein the optical substratecomprises an optically transparent film having a second surface oppositeto the first surface, the second surface being smooth.
 12. The opticalsubstrate of claim 4, wherein the flinctionfis selected from the groupof mathematical functions consisting of triangular function, sawtoothfunction and square wave function.
 13. A backlight display devicecomprising: a light source for generating light; a light guide forguiding the light therealong including a reflective surface forreflecting the light out of the light guide; and an optical filmcomprising: at least one surface, said at least one surface comprisingat least one optical structure having a shape and dimensions, whereinthe shape and dimensions of each optical structure represents in part amodulation of a corresponding idealized structure, and wherein saidshape and dimensions of each of said at least one optical structure isdetermined in part by at least one randomly generated component ofmodulation wherein the modulation of each of said at least one opticalstructure is limited by a neighboring optical structure comprised by thesurface.
 14. The backlight display device of in claim 13 wherein said atleast one optical structure represents an idealized prismatic structurefollowing a surface path modulated by a mathematical function (1)y _(i) =A _(i)sin{φλ−Φ_(i) }+S _(i)  (1) defined relative to a segment Cof a coordinate system, wherein i is an integer indicative of the i^(th)surface path, y_(i) is an instantaneous displacement of the pathrelative to C on the i^(th) path, A_(i) is an amplitude scaling factorof the i^(th) path relative to C, S_(i) is a shift in a startingposition of y_(i), φ is a number between zero and 2π inclusive, λ is awavelength which is a real number, Φ_(i) is a phase component for thei^(th) path, whereinΦ_(i)=Φ_(i−1) +Q _(i) Δ+R _(i)δ  (2) where Q_(i) is a randomly or pseudorandomly chosen number having a value of 1 or −1 R_(i) is a continuousrandom variable between −1 and 1, each defined for the i^(th) path, andΔ and δ are real numbers that define a magnitude of a phase steppingcomponent and a magnitude of a phase dither component, respectively. 15.The backlight display device of claim 13 wherein said at least oneoptical structure represents an idealized prismatic structure followinga surface path modulated by a mathematical function (3a) $\begin{matrix}{y_{i} = {{\sum\limits_{k = 1}^{n}{A_{i,k}\sin\left\{ {{\phi\;\lambda_{k}} - \Phi_{i,k}} \right\}}} + S_{i}}} & \left( {3a} \right)\end{matrix}$ defined relative to a segment C of a coordinate system,wherein i is an integer indicative of the i^(th) surface path, y_(i) isan instantaneous displacement of the path relative to C on the i^(th)path, A_(i,k) is the k^(th) amplitude scaling factor of the i^(th) pathrelative to C, S_(i) is a shift in a starting position of y_(i), φ is anumber between zero and 2π inclusive, n is an integer greater than 1,each wavelength λ_(k) is a real number, Φ_(i,k) is the k^(th) phasecomponent of the i^(th) path, whereinΦ_(i,k)=Φ_(i−i,k) +Q _(i,k) Δ+R _(i,k)δ  (3b) Q_(i,k) is the k^(th)randomly or pseudo randomly chosen number having a value of 1 or −1 forthe i^(th) path, R_(i,k) is the k^(th) continuous random variable avalue between −1 and 1 for the i^(th) path, and Δ and δ are real numbersthat define a magnitude of a phase stepping component and a magnitude ofa phase dither component, respectively.
 16. The backlight display deviceof claim 13 wherein said at least one optical structure represents anidealized prismatic structure following a surface path modulated by amathematical functiony _(i) =A _(i)[(1−m)r _(i)(φ)+m r _(i−1)(φ)]+S _(i) wherein i and i−1are indicative of an i^(th) and a(i−1)^(th) path, respectively, thei^(th) and the (i−1)^(th) paths being adjacent paths, the i^(th) and the(i−1)^(th) path amplitudes being mixed, wherein part of a random vectorfor y_(i−1) is added to y_(i) for the i^(th) path, wherein r_(i)(φ) is aband-limited random or pseudo random function of φ for each i^(th) path,r_(i)(φ) has a continuously varying yalue between −1 and 1; φ is 0 to 2πinclusive; m is a scalar mixing parameter with a value between 0 and 1;A_(i) is an amplitude scaling parameter; and S_(i) is a shift in astarting position of y_(i).
 17. The backlight display device of claim 15wherein S_(i)–S_(i−1) is in the range of 5 μm to 200 μm.
 18. Thebacklight display device of claim 15 wherein the prismatic structure hasan apex angle of between 20 degrees and 160 degrees.
 19. An opticalsubstrate according to claim 1 wherein said at least one opticalstructure represents an idealized prismatic structure.
 20. An opticalsubstrate according to claim 1 wherein said at least one opticalstructure represents an idealized structure characterized by a function,wherein a phase of the function is randomly or pseudo randomlymodulated.